graphite-dependences.c (reduction_dr_1): New.

[gcc.git] / gcc / graphite-dependences.c

/* Data dependence analysis for Graphite.
   Copyright (C) 2009 Free Software Foundation, Inc.
   Contributed by Sebastian Pop <sebastian.pop@amd.com> and
   Konrad Trifunovic <konrad.trifunovic@inria.fr>.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3, or (at your option)
any later version.

GCC is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3.  If not see
<http://www.gnu.org/licenses/>.  */

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "ggc.h"
#include "tree.h"
#include "rtl.h"
#include "basic-block.h"
#include "diagnostic.h"
#include "tree-flow.h"
#include "toplev.h"
#include "tree-dump.h"
#include "timevar.h"
#include "cfgloop.h"
#include "tree-chrec.h"
#include "tree-data-ref.h"
#include "tree-scalar-evolution.h"
#include "tree-pass.h"
#include "domwalk.h"
#include "pointer-set.h"
#include "gimple.h"

#ifdef HAVE_cloog
#include "cloog/cloog.h"
#include "ppl_c.h"
#include "sese.h"
#include "graphite-ppl.h"
#include "graphite.h"
#include "graphite-poly.h"
#include "graphite-dependences.h"

/* Returns a new polyhedral Data Dependence Relation (DDR).  SOURCE is
   the source data reference, SINK is the sink data reference.  SOURCE
   and SINK define an edge in the Data Dependence Graph (DDG).  */

static poly_ddr_p
new_poly_ddr (poly_dr_p source, poly_dr_p sink,
              ppl_Pointset_Powerset_C_Polyhedron_t ddp)
{
  poly_ddr_p pddr;

  pddr = XNEW (struct poly_ddr);
  PDDR_SOURCE (pddr) = source;
  PDDR_SINK (pddr) = sink;
  PDDR_DDP (pddr) = ddp;
  PDDR_KIND (pddr) = unknown_dependence;

  return pddr;
}

/* Free the poly_ddr_p P.  */

void
free_poly_ddr (void *p)
{
  poly_ddr_p pddr = (poly_ddr_p) p;
  ppl_delete_Pointset_Powerset_C_Polyhedron (PDDR_DDP (pddr));
  free (pddr);
}

/* Comparison function for poly_ddr hash table.  */

int
eq_poly_ddr_p (const void *pddr1, const void *pddr2)
{
  const struct poly_ddr *p1 = (const struct poly_ddr *) pddr1;
  const struct poly_ddr *p2 = (const struct poly_ddr *) pddr2;

  return (PDDR_SOURCE (p1) == PDDR_SOURCE (p2)
          && PDDR_SINK (p1) == PDDR_SINK (p2));
}

/* Hash function for poly_ddr hashtable.  */

hashval_t
hash_poly_ddr_p (const void *pddr)
{
  const struct poly_ddr *p = (const struct poly_ddr *) pddr;

  return (hashval_t) ((long) PDDR_SOURCE (p) + (long) PDDR_SINK (p));
}

/* Returns true when PDDR has no dependence.  */

static bool
pddr_is_empty (poly_ddr_p pddr)
{
  if (PDDR_KIND (pddr) != unknown_dependence)
    return PDDR_KIND (pddr) == no_dependence ? true : false;

  if (ppl_Pointset_Powerset_C_Polyhedron_is_empty (PDDR_DDP (pddr)))
    {
      PDDR_KIND (pddr) = no_dependence;
      return true;
    }

  PDDR_KIND (pddr) = has_dependence;
  return false;
}

/* Returns a polyhedron of dimension DIM.

   Maps the dimensions [0, ..., cut - 1] of polyhedron P to OFFSET0
   and the dimensions [cut, ..., nb_dim] to DIM - GDIM.  */

static ppl_Pointset_Powerset_C_Polyhedron_t
map_into_dep_poly (graphite_dim_t dim, graphite_dim_t gdim,
                   ppl_Pointset_Powerset_C_Polyhedron_t p,
                   graphite_dim_t cut,
                   graphite_dim_t offset)
{
  ppl_Pointset_Powerset_C_Polyhedron_t res;

  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
    (&res, p);
  ppl_insert_dimensions_pointset (res, 0, offset);
  ppl_insert_dimensions_pointset (res, offset + cut,
                                  dim - offset - cut - gdim);

  return res;
}

/* Swap [cut0, ..., cut1] to the end of DR: "a CUT0 b CUT1 c" is
   transformed into "a CUT0 c CUT1' b"

   Add NB0 zeros before "a":  "00...0 a CUT0 c CUT1' b"
   Add NB1 zeros between "a" and "c":  "00...0 a 00...0 c CUT1' b"
   Add DIM - NB0 - NB1 - PDIM zeros between "c" and "b":
   "00...0 a 00...0 c 00...0 b".  */

static ppl_Pointset_Powerset_C_Polyhedron_t
map_dr_into_dep_poly (graphite_dim_t dim,
                      ppl_Pointset_Powerset_C_Polyhedron_t dr,
                      graphite_dim_t cut0, graphite_dim_t cut1,
                      graphite_dim_t nb0, graphite_dim_t nb1)
{
  ppl_dimension_type pdim;
  ppl_dimension_type *map;
  ppl_Pointset_Powerset_C_Polyhedron_t res;
  ppl_dimension_type i;

  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
    (&res, dr);
  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (res, &pdim);

  map = (ppl_dimension_type *) XNEWVEC (ppl_dimension_type, pdim);

  /* First mapping: move 'g' vector to right position.  */
  for (i = 0; i < cut0; i++)
    map[i] = i;

  for (i = cut0; i < cut1; i++)
    map[i] = pdim - cut1 + i;

  for (i = cut1; i < pdim; i++)
    map[i] = cut0 + i - cut1;

  ppl_Pointset_Powerset_C_Polyhedron_map_space_dimensions (res, map, pdim);
  free (map);

  /* After swapping 's' and 'g' vectors, we have to update a new cut.  */
  cut1 = pdim - cut1 + cut0;

  ppl_insert_dimensions_pointset (res, 0, nb0);
  ppl_insert_dimensions_pointset (res, nb0 + cut0, nb1);
  ppl_insert_dimensions_pointset (res, nb0 + nb1 + cut1,
                                  dim - nb0 - nb1 - pdim);

  return res;
}

/* Builds a constraints of the form "POS1 - POS2 CSTR_TYPE C" */

static ppl_Constraint_t
build_pairwise_constraint (graphite_dim_t dim,
                           graphite_dim_t pos1, graphite_dim_t pos2,
                           int c, enum ppl_enum_Constraint_Type cstr_type)
{
  ppl_Linear_Expression_t expr;
  ppl_Constraint_t cstr;
  ppl_Coefficient_t coef;
  Value v, v_op, v_c;

  value_init (v);
  value_init (v_op);
  value_init (v_c);

  value_set_si (v, 1);
  value_set_si (v_op, -1);
  value_set_si (v_c, c);

  ppl_new_Coefficient (&coef);
  ppl_new_Linear_Expression_with_dimension (&expr, dim);

  ppl_assign_Coefficient_from_mpz_t (coef, v);
  ppl_Linear_Expression_add_to_coefficient (expr, pos1, coef);
  ppl_assign_Coefficient_from_mpz_t (coef, v_op);
  ppl_Linear_Expression_add_to_coefficient (expr, pos2, coef);
  ppl_assign_Coefficient_from_mpz_t (coef, v_c);
  ppl_Linear_Expression_add_to_inhomogeneous (expr, coef);

  ppl_new_Constraint (&cstr, expr, cstr_type);

  ppl_delete_Linear_Expression (expr);
  ppl_delete_Coefficient (coef);
  value_clear (v);
  value_clear (v_op);
  value_clear (v_c);

  return cstr;
}

/* Builds subscript equality constraints.  */

static ppl_Pointset_Powerset_C_Polyhedron_t
dr_equality_constraints (graphite_dim_t dim,
                         graphite_dim_t pos, graphite_dim_t nb_subscripts)
{
  ppl_Polyhedron_t subscript_equalities;
  ppl_Pointset_Powerset_C_Polyhedron_t res;
  Value v, v_op;
  graphite_dim_t i;

  value_init (v);
  value_init (v_op);
  value_set_si (v, 1);
  value_set_si (v_op, -1);

  ppl_new_C_Polyhedron_from_space_dimension (&subscript_equalities, dim, 0);
  for (i = 0; i < nb_subscripts; i++)
    {
      ppl_Linear_Expression_t expr;
      ppl_Constraint_t cstr;
      ppl_Coefficient_t coef;

      ppl_new_Coefficient (&coef);
      ppl_new_Linear_Expression_with_dimension (&expr, dim);

      ppl_assign_Coefficient_from_mpz_t (coef, v);
      ppl_Linear_Expression_add_to_coefficient (expr, pos + i, coef);
      ppl_assign_Coefficient_from_mpz_t (coef, v_op);
      ppl_Linear_Expression_add_to_coefficient (expr, pos + i + nb_subscripts,
                                                coef);

      ppl_new_Constraint (&cstr, expr, PPL_CONSTRAINT_TYPE_EQUAL);
      ppl_Polyhedron_add_constraint (subscript_equalities, cstr);

      ppl_delete_Linear_Expression (expr);
      ppl_delete_Constraint (cstr);
      ppl_delete_Coefficient (coef);
    }

  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron
    (&res, subscript_equalities);
  value_clear (v);
  value_clear (v_op);
  ppl_delete_Polyhedron (subscript_equalities);

  return res;
}

/* Builds scheduling equality constraints.  */

static ppl_Pointset_Powerset_C_Polyhedron_t
build_pairwise_scheduling_equality (graphite_dim_t dim,
                                    graphite_dim_t pos, graphite_dim_t offset)
{
  ppl_Pointset_Powerset_C_Polyhedron_t res;
  ppl_Polyhedron_t equalities;
  ppl_Constraint_t cstr;

  ppl_new_C_Polyhedron_from_space_dimension (&equalities, dim, 0);

  cstr = build_pairwise_constraint (dim, pos, pos + offset, 0,
                                    PPL_CONSTRAINT_TYPE_EQUAL);
  ppl_Polyhedron_add_constraint (equalities, cstr);
  ppl_delete_Constraint (cstr);

  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&res, equalities);
  ppl_delete_Polyhedron (equalities);
  return res;
}

/* Builds scheduling inequality constraints.  */

static ppl_Pointset_Powerset_C_Polyhedron_t
build_pairwise_scheduling_inequality (graphite_dim_t dim,
                                      graphite_dim_t pos,
                                      graphite_dim_t offset,
                                      bool direction)
{
  ppl_Pointset_Powerset_C_Polyhedron_t res;
  ppl_Polyhedron_t equalities;
  ppl_Constraint_t cstr;

  ppl_new_C_Polyhedron_from_space_dimension (&equalities, dim, 0);

  if (direction)
    cstr = build_pairwise_constraint (dim, pos, pos + offset, -1,
                                      PPL_CONSTRAINT_TYPE_GREATER_OR_EQUAL);
  else
    cstr = build_pairwise_constraint (dim, pos, pos + offset, 1,
                                      PPL_CONSTRAINT_TYPE_LESS_OR_EQUAL);

  ppl_Polyhedron_add_constraint (equalities, cstr);
  ppl_delete_Constraint (cstr);

  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&res, equalities);
  ppl_delete_Polyhedron (equalities);
  return res;
}

/* Returns true when adding the lexicographical constraints at level I
   to the RES dependence polyhedron returns an empty polyhedron.  */

static bool
lexicographically_gt_p (ppl_Pointset_Powerset_C_Polyhedron_t res,
                        graphite_dim_t dim,
                        graphite_dim_t offset,
                        bool direction, graphite_dim_t i)
{
  ppl_Pointset_Powerset_C_Polyhedron_t ineq;
  bool empty_p;

  ineq = build_pairwise_scheduling_inequality (dim, i, offset,
                                               direction);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (ineq, res);
  empty_p = ppl_Pointset_Powerset_C_Polyhedron_is_empty (ineq);
  if (!empty_p)
    ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, ineq);
  ppl_delete_Pointset_Powerset_C_Polyhedron (ineq);

  return !empty_p;
}

/* Build the precedence constraints for the lexicographical comparison
   of time vectors RES following the lexicographical order.  */

static void
build_lexicographically_gt_constraint (ppl_Pointset_Powerset_C_Polyhedron_t *res,
                                       graphite_dim_t dim,
                                       graphite_dim_t tdim1,
                                       graphite_dim_t offset,
                                       bool direction)
{
  graphite_dim_t i;

  if (lexicographically_gt_p (*res, dim, offset, direction, 0))
    return;

  for (i = 0; i < tdim1 - 1; i++)
    {
      ppl_Pointset_Powerset_C_Polyhedron_t sceq;

      sceq = build_pairwise_scheduling_equality (dim, i, offset);
      ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (*res, sceq);
      ppl_delete_Pointset_Powerset_C_Polyhedron (sceq);

      if (lexicographically_gt_p (*res, dim, offset, direction, i + 1))
        return;
    }

  if (i == tdim1 - 1)
    {
      ppl_delete_Pointset_Powerset_C_Polyhedron (*res);
      ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (res, dim, 1);
    }
}

/* Build the dependence polyhedron for data references PDR1 and PDR2.  */

static poly_ddr_p
dependence_polyhedron_1 (poly_bb_p pbb1, poly_bb_p pbb2,
                         ppl_Pointset_Powerset_C_Polyhedron_t d1,
                         ppl_Pointset_Powerset_C_Polyhedron_t d2,
                         poly_dr_p pdr1, poly_dr_p pdr2,
                         ppl_Polyhedron_t s1, ppl_Polyhedron_t s2,
                         bool direction,
                         bool original_scattering_p)
{
  scop_p scop = PBB_SCOP (pbb1);
  graphite_dim_t tdim1 = original_scattering_p ?
    pbb_nb_scattering_orig (pbb1) : pbb_nb_scattering_transform (pbb1);
  graphite_dim_t tdim2 = original_scattering_p ?
    pbb_nb_scattering_orig (pbb2) : pbb_nb_scattering_transform (pbb2);
  graphite_dim_t ddim1 = pbb_dim_iter_domain (pbb1);
  graphite_dim_t ddim2 = pbb_dim_iter_domain (pbb2);
  graphite_dim_t sdim1 = PDR_NB_SUBSCRIPTS (pdr1) + 1;
  graphite_dim_t gdim = scop_nb_params (scop);
  graphite_dim_t dim1 = pdr_dim (pdr1);
  graphite_dim_t dim2 = pdr_dim (pdr2);
  graphite_dim_t dim = tdim1 + tdim2 + dim1 + dim2;
  ppl_Pointset_Powerset_C_Polyhedron_t res;
  ppl_Pointset_Powerset_C_Polyhedron_t id1, id2, isc1, isc2, idr1, idr2;
  ppl_Pointset_Powerset_C_Polyhedron_t sc1, sc2, dreq;

  gcc_assert (PBB_SCOP (pbb1) == PBB_SCOP (pbb2));
  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&sc1, s1);
  ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron (&sc2, s2);

  id1 = map_into_dep_poly (dim, gdim, d1, ddim1, tdim1);
  id2 = map_into_dep_poly (dim, gdim, d2, ddim2, tdim1 + ddim1 + tdim2);
  isc1 = map_into_dep_poly (dim, gdim, sc1, ddim1 + tdim1, 0);
  isc2 = map_into_dep_poly (dim, gdim, sc2, ddim2 + tdim2, tdim1 + ddim1);

  idr1 = map_dr_into_dep_poly (dim, PDR_ACCESSES (pdr1), ddim1, ddim1 + gdim,
                               tdim1, tdim2 + ddim2);
  idr2 = map_dr_into_dep_poly (dim, PDR_ACCESSES (pdr2), ddim2, ddim2 + gdim,
                               tdim1 + ddim1 + tdim2, sdim1);

  /* Now add the subscript equalities.  */
  dreq = dr_equality_constraints (dim, tdim1 + ddim1 + tdim2 + ddim2, sdim1);

  ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (&res, dim, 0);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, id1);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, id2);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, isc1);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, isc2);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, idr1);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, idr2);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (res, dreq);
  ppl_delete_Pointset_Powerset_C_Polyhedron (id1);
  ppl_delete_Pointset_Powerset_C_Polyhedron (id2);
  ppl_delete_Pointset_Powerset_C_Polyhedron (sc1);
  ppl_delete_Pointset_Powerset_C_Polyhedron (sc2);
  ppl_delete_Pointset_Powerset_C_Polyhedron (isc1);
  ppl_delete_Pointset_Powerset_C_Polyhedron (isc2);
  ppl_delete_Pointset_Powerset_C_Polyhedron (idr1);
  ppl_delete_Pointset_Powerset_C_Polyhedron (idr2);
  ppl_delete_Pointset_Powerset_C_Polyhedron (dreq);

  if (!ppl_Pointset_Powerset_C_Polyhedron_is_empty (res))
    build_lexicographically_gt_constraint (&res, dim, MIN (tdim1, tdim2),
                                           tdim1 + ddim1, direction);

  return new_poly_ddr (pdr1, pdr2, res);
}

/* Build the dependence polyhedron for data references PDR1 and PDR2.
   If possible use already cached information.  */

static poly_ddr_p
dependence_polyhedron (poly_bb_p pbb1, poly_bb_p pbb2,
                       ppl_Pointset_Powerset_C_Polyhedron_t d1,
                       ppl_Pointset_Powerset_C_Polyhedron_t d2,
                       poly_dr_p pdr1, poly_dr_p pdr2,
                       ppl_Polyhedron_t s1, ppl_Polyhedron_t s2,
                       bool direction,
                       bool original_scattering_p)
{
  PTR *x = NULL;
  poly_ddr_p res;

  if (original_scattering_p)
    {
      struct poly_ddr tmp;

      tmp.source = pdr1;
      tmp.sink = pdr2;
      x = htab_find_slot (SCOP_ORIGINAL_PDDRS (PBB_SCOP (pbb1)),
                          &tmp, INSERT);

      if (x && *x)
        return (poly_ddr_p) *x;
    }

  res = dependence_polyhedron_1 (pbb1, pbb2, d1, d2, pdr1, pdr2,
                                 s1, s2, direction, original_scattering_p);

  if (original_scattering_p)
    *x = res;

  return res;
}

static bool
poly_drs_may_alias_p (poly_dr_p pdr1, poly_dr_p pdr2);

/* Returns the PDDR corresponding to the original schedule, or NULL if
   the dependence relation is empty or unknown (Can't judge dependency
   under polyhedral model.  */

static poly_ddr_p
pddr_original_scattering (poly_bb_p pbb1, poly_bb_p pbb2,
                          poly_dr_p pdr1, poly_dr_p pdr2)
{
  poly_ddr_p pddr;
  ppl_Pointset_Powerset_C_Polyhedron_t d1 = PBB_DOMAIN (pbb1);
  ppl_Pointset_Powerset_C_Polyhedron_t d2 = PBB_DOMAIN (pbb2);
  ppl_Polyhedron_t so1 = PBB_ORIGINAL_SCATTERING (pbb1);
  ppl_Polyhedron_t so2 = PBB_ORIGINAL_SCATTERING (pbb2);

  if ((pdr_read_p (pdr1) && pdr_read_p (pdr2))
      || PDR_BASE_OBJECT_SET (pdr1) != PDR_BASE_OBJECT_SET (pdr2)
      || PDR_NB_SUBSCRIPTS (pdr1) != PDR_NB_SUBSCRIPTS (pdr2))
    return NULL;

  pddr = dependence_polyhedron (pbb1, pbb2, d1, d2, pdr1, pdr2, so1, so2,
                                true, true);
  if (pddr_is_empty (pddr))
    return NULL;

  return pddr;
}

/* Return true when the data dependence relation between the data
   references PDR1 belonging to PBB1 and PDR2 is part of a
   reduction.  */

static inline bool
reduction_dr_1 (poly_bb_p pbb1, poly_dr_p pdr1, poly_dr_p pdr2)
{
  int i;
  poly_dr_p pdr;

  /* PBB1 should be a reduction PBB.  Reduction PBBs should have only
     one write.  */
  gcc_assert (PBB_IS_REDUCTION (pbb1)
              && number_of_write_pdrs (pbb1) == 1);

  for (i = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb1), i, pdr); i++)
    if (PDR_TYPE (pdr) == PDR_WRITE)
      break;

  return same_pdr_p (pdr, pdr1) && same_pdr_p (pdr, pdr2);
}

/* Return true when the data dependence relation between the data
   references PDR1 belonging to PBB1 and PDR2 belonging to PBB2 is
   part of a reduction.  */

static inline bool
reduction_dr_p (poly_bb_p pbb1, poly_bb_p pbb2,
                poly_dr_p pdr1, poly_dr_p pdr2)
{
  if (PBB_IS_REDUCTION (pbb1))
    return reduction_dr_1 (pbb1, pdr1, pdr2);

  if (PBB_IS_REDUCTION (pbb2))
    return reduction_dr_1 (pbb2, pdr2, pdr1);

  return false;
}

/* Returns true when the PBB_TRANSFORMED_SCATTERING functions of PBB1
   and PBB2 respect the data dependences of PBB_ORIGINAL_SCATTERING
   functions.  */

static bool
graphite_legal_transform_dr (poly_bb_p pbb1, poly_bb_p pbb2,
                             poly_dr_p pdr1, poly_dr_p pdr2)
{
  ppl_Polyhedron_t st1, st2;
  ppl_Pointset_Powerset_C_Polyhedron_t po, pt;
  graphite_dim_t ddim1, otdim1, otdim2, ttdim1, ttdim2;
  ppl_Pointset_Powerset_C_Polyhedron_t temp;
  ppl_dimension_type pdim;
  bool is_empty_p;
  poly_ddr_p pddr;
  ppl_Pointset_Powerset_C_Polyhedron_t d1 = PBB_DOMAIN (pbb1);
  ppl_Pointset_Powerset_C_Polyhedron_t d2 = PBB_DOMAIN (pbb2);

  if (reduction_dr_p (pbb1, pbb2, pdr1, pdr2))
    return true;

  pddr = pddr_original_scattering (pbb1, pbb2, pdr1, pdr2);
  if (!pddr)
    return true;

  po = PDDR_DDP (pddr);

  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, "\nloop carries dependency.\n");

  st1 = PBB_TRANSFORMED_SCATTERING (pbb1);
  st2 = PBB_TRANSFORMED_SCATTERING (pbb2);
  ddim1 = pbb_dim_iter_domain (pbb1);
  otdim1 = pbb_nb_scattering_orig (pbb1);
  otdim2 = pbb_nb_scattering_orig (pbb2);
  ttdim1 = pbb_nb_scattering_transform (pbb1);
  ttdim2 = pbb_nb_scattering_transform (pbb2);

  /* Copy the PO polyhedron into the TEMP, so it is not destroyed.
     Keep in mind, that PO polyhedron might be restored from the cache
     and should not be modified!  */
  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (po, &pdim);
  ppl_new_Pointset_Powerset_C_Polyhedron_from_space_dimension (&temp, pdim, 0);
  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (temp, po);

  pddr = dependence_polyhedron (pbb1, pbb2, d1, d2, pdr1, pdr2, st1, st2,
                                false, false);
  pt = PDDR_DDP (pddr);

  /* Extend PO and PT to have the same dimensions.  */
  ppl_insert_dimensions_pointset (temp, otdim1, ttdim1);
  ppl_insert_dimensions_pointset (temp, otdim1 + ttdim1 + ddim1 + otdim2, ttdim2);
  ppl_insert_dimensions_pointset (pt, 0, otdim1);
  ppl_insert_dimensions_pointset (pt, otdim1 + ttdim1 + ddim1, otdim2);

  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (temp, pt);
  is_empty_p = ppl_Pointset_Powerset_C_Polyhedron_is_empty (temp);

  ppl_delete_Pointset_Powerset_C_Polyhedron (temp);
  free_poly_ddr (pddr);

  return is_empty_p;
}

/* Return true when the data dependence relation for PBB1 and PBB2 is
   part of a reduction.  */

static inline bool
reduction_ddr_p (poly_bb_p pbb1, poly_bb_p pbb2)
{
  return pbb1 == pbb2 && PBB_IS_REDUCTION (pbb1);
}

/* Iterates over the data references of PBB1 and PBB2 and detect
   whether the transformed schedule is correct.  */

static bool
graphite_legal_transform_bb (poly_bb_p pbb1, poly_bb_p pbb2)
{
  int i, j;
  poly_dr_p pdr1, pdr2;

  if (!PBB_PDR_DUPLICATES_REMOVED (pbb1))
    pbb_remove_duplicate_pdrs (pbb1);

  if (!PBB_PDR_DUPLICATES_REMOVED (pbb2))
    pbb_remove_duplicate_pdrs (pbb2);

  if (reduction_ddr_p (pbb1, pbb2))
    return true;

  for (i = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb1), i, pdr1); i++)
    for (j = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb2), j, pdr2); j++)
      if (!graphite_legal_transform_dr (pbb1, pbb2, pdr1, pdr2))
        return false;

  return true;
}

/* Iterates over the SCOP and detect whether the transformed schedule
   is correct.  */

bool
graphite_legal_transform (scop_p scop)
{
  int i, j;
  poly_bb_p pbb1, pbb2;

  timevar_push (TV_GRAPHITE_DATA_DEPS);

  for (i = 0; VEC_iterate (poly_bb_p, SCOP_BBS (scop), i, pbb1); i++)
    for (j = 0; VEC_iterate (poly_bb_p, SCOP_BBS (scop), j, pbb2); j++)
      if (!graphite_legal_transform_bb (pbb1, pbb2))
        {
          timevar_pop (TV_GRAPHITE_DATA_DEPS);
          return false;
        }

  timevar_pop (TV_GRAPHITE_DATA_DEPS);
  return true;
}

/* Remove all the dimensions except alias information at dimension
   ALIAS_DIM.  */

static void
build_alias_set_powerset (ppl_Pointset_Powerset_C_Polyhedron_t alias_powerset,
                          ppl_dimension_type alias_dim)
{
  ppl_dimension_type *ds;
  ppl_dimension_type access_dim;
  unsigned i, pos = 0;

  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (alias_powerset,
                                                      &access_dim);
  ds = XNEWVEC (ppl_dimension_type, access_dim-1);
  for (i = 0; i < access_dim; i++)
    {
      if (i == alias_dim)
        continue;

      ds[pos] = i;
      pos++;
    }

  ppl_Pointset_Powerset_C_Polyhedron_remove_space_dimensions (alias_powerset,
                                                              ds,
                                                              access_dim - 1);
  free (ds);
}

/* Return true when PDR1 and PDR2 may alias.  */

static bool
poly_drs_may_alias_p (poly_dr_p pdr1, poly_dr_p pdr2)
{
  ppl_Pointset_Powerset_C_Polyhedron_t alias_powerset1, alias_powerset2;
  ppl_Pointset_Powerset_C_Polyhedron_t accesses1 = PDR_ACCESSES (pdr1);
  ppl_Pointset_Powerset_C_Polyhedron_t accesses2 = PDR_ACCESSES (pdr2);
  ppl_dimension_type alias_dim1 = pdr_alias_set_dim (pdr1);
  ppl_dimension_type alias_dim2 = pdr_alias_set_dim (pdr2);
  int empty_p;

  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
    (&alias_powerset1, accesses1);
  ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
    (&alias_powerset2, accesses2);

  build_alias_set_powerset (alias_powerset1, alias_dim1);
  build_alias_set_powerset (alias_powerset2, alias_dim2);

  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign
    (alias_powerset1, alias_powerset2);

  empty_p = ppl_Pointset_Powerset_C_Polyhedron_is_empty (alias_powerset1);

  ppl_delete_Pointset_Powerset_C_Polyhedron (alias_powerset1);
  ppl_delete_Pointset_Powerset_C_Polyhedron (alias_powerset2);

  return !empty_p;
}

/* Returns TRUE when the dependence polyhedron between PDR1 and
   PDR2 represents a loop carried dependence at level LEVEL.  */

static bool
graphite_carried_dependence_level_k (poly_dr_p pdr1, poly_dr_p pdr2,
                                     int level)
{
  poly_bb_p pbb1 = PDR_PBB (pdr1);
  poly_bb_p pbb2 = PDR_PBB (pdr2);
  ppl_Pointset_Powerset_C_Polyhedron_t d1 = PBB_DOMAIN (pbb1);
  ppl_Pointset_Powerset_C_Polyhedron_t d2 = PBB_DOMAIN (pbb2);
  ppl_Polyhedron_t so1 = PBB_TRANSFORMED_SCATTERING (pbb1);
  ppl_Polyhedron_t so2 = PBB_TRANSFORMED_SCATTERING (pbb2);
  ppl_Pointset_Powerset_C_Polyhedron_t po;
  ppl_Pointset_Powerset_C_Polyhedron_t eqpp;
  graphite_dim_t tdim1 = pbb_nb_scattering_transform (pbb1);
  graphite_dim_t ddim1 = pbb_dim_iter_domain (pbb1);
  ppl_dimension_type dim;
  bool empty_p;
  poly_ddr_p pddr;
  int obj_base_set1 = PDR_BASE_OBJECT_SET (pdr1);
  int obj_base_set2 = PDR_BASE_OBJECT_SET (pdr2);

  if ((pdr_read_p (pdr1) && pdr_read_p (pdr2))
      || !poly_drs_may_alias_p (pdr1, pdr2))
    return false;

  if (obj_base_set1 != obj_base_set2)
    return true;

  if (PDR_NB_SUBSCRIPTS (pdr1) != PDR_NB_SUBSCRIPTS (pdr2))
    return false;

  pddr = dependence_polyhedron (pbb1, pbb2, d1, d2, pdr1, pdr2, so1, so2,
                                true, false);

  if (pddr_is_empty (pddr))
    return false;

  po = PDDR_DDP (pddr);
  ppl_Pointset_Powerset_C_Polyhedron_space_dimension (po, &dim);
  eqpp = build_pairwise_scheduling_inequality (dim, level, tdim1 + ddim1, 1);

  ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (eqpp, po);
  empty_p = ppl_Pointset_Powerset_C_Polyhedron_is_empty (eqpp);

  ppl_delete_Pointset_Powerset_C_Polyhedron (eqpp);
  return !empty_p;
}

/* Check data dependency between PBB1 and PBB2 at level LEVEL.  */

bool
dependency_between_pbbs_p (poly_bb_p pbb1, poly_bb_p pbb2, int level)
{
  int i, j;
  poly_dr_p pdr1, pdr2;

  timevar_push (TV_GRAPHITE_DATA_DEPS);

  for (i = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb1), i, pdr1); i++)
    for (j = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb2), j, pdr2); j++)
      if (graphite_carried_dependence_level_k (pdr1, pdr2, level))
        {
          timevar_pop (TV_GRAPHITE_DATA_DEPS);
          return true;
        }

  timevar_pop (TV_GRAPHITE_DATA_DEPS);
  return false;
}

/* Pretty print to FILE all the data dependences of SCoP in DOT
   format.  */

static void
dot_deps_1 (FILE *file, scop_p scop)
{
  int i, j, k, l;
  poly_bb_p pbb1, pbb2;
  poly_dr_p pdr1, pdr2;

  fputs ("digraph all {\n", file);

  for (i = 0; VEC_iterate (poly_bb_p, SCOP_BBS (scop), i, pbb1); i++)
    for (j = 0; VEC_iterate (poly_bb_p, SCOP_BBS (scop), j, pbb2); j++)
      for (k = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb1), k, pdr1); k++)
        for (l = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb2), l, pdr2); l++)
          if (pddr_original_scattering (pbb1, pbb2, pdr1, pdr2))
            fprintf (file, "S%d_D%d -> S%d_D%d\n",
                     pbb_index (pbb1), PDR_ID (pdr1),
                     pbb_index (pbb2), PDR_ID (pdr2));

  fputs ("}\n\n", file);
}

/* Display all the data dependences in SCoP using dotty.  */

void
dot_deps (scop_p scop)
{
  /* When debugging, enable the following code.  This cannot be used
     in production compilers because it calls "system".  */
#if 0
  int x;
  FILE *stream = fopen ("/tmp/scopdeps.dot", "w");
  gcc_assert (stream);

  dot_deps_1 (stream, scop);
  fclose (stream);

  x = system ("dotty /tmp/scopdeps.dot");
#else
  dot_deps_1 (stderr, scop);
#endif
}


#endif